Light rays reaching the eye

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Assume I am standing in a desert at night (It's pitch dark). I have an opaque white object in front of me inclined at 45 degrees (see diagram). I now turn on a point light source next to me.

http://img199.imageshack.us/img199/8945/lightt.jpg [Broken]

When I imagine the scene I feel I will be able to see point P on the object in front of me, at least a certain shade of white (grayish).

However, when I think of this from a physics point of view, there is no ray of light from the light source that hits point P and then reflects to my eye (considering angle of incidence = angle of reflection).

When I trace the ray from the eye to point P and toward the reflecting source I seem to go to inifnity (there is no wall there to reflect any light as it is a desert).

So in reality will any shade of white on point P be visible to the observer? If yes, then which ray of light does it come from and how does it reach the eye?
 
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  • #2
russ_watters
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Angle of incidence only equals angle of reflection for a mirror. Diffuse reflection reflects the light in all directions.
 
  • #3
Mentallic
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Is it not possible to have a mirror with colour film over it (just as an indicator that you're seeing point P) or even a mostly opaque surface that doesn't diffuse reflection?
 
  • #4
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Angle of incidence only equals angle of reflection for a mirror. Diffuse reflection reflects the light in all directions.
Ahhh... but isn't diffuse reflection a consequence of rough surfaces? If the object was very glossy/smooth then would it still be seen?
 
  • #5
But there are lots of other objects around like sand that will catch a little of the point source of light, and then bounce off the glossy screen and into your retina.
 
  • #6
russ_watters
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Ahhh... but isn't diffuse reflection a consequence of rough surfaces? If the object was very glossy/smooth then would it still be seen?
I'm not sure what the exact mechanism is, but you specified white, not mirrored in your first post...
 
  • #7
DaveC426913
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Note that a point source of light still emits in all directions. Your diagram is incomplete in that it does not show any other rays of light - but there exists a ray of light from that source that will reach the eye. You would see the point of light in the reflection.

What I think you're asking about is a collimated source, such as a laser. That's what you'd need to use in order for your diagram to be representative.

And as we know, the beam form a laser is invisible unless it enters your eye - whether directly, or indirectly through some type of scattering.
 
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  • #8
Mentallic
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I'm not sure what the exact mechanism is, but you specified white, not mirrored in your first post...
Again, can't it be possible to have a white surface that doesn't diffuse reflection? It would rather act like a mirror.

What I think you're asking about is a collimated source, such as a laser. That's what you'd need to use in order for your diagram to be representative.

And as we know, the beam form a laser is invisible unless it enters your eye - whether directly, or indirectly through some type of scattering.
Well now I'm convinced.
 
  • #9
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Note that a point source of light still emits in all directions. Your diagram is incomplete in that it does not show any other rays of light - but there exists a ray of light from that source that will reach the eye. You would see the point of light in the reflection.
The only ray of light that I have shown in the diagram is the one which hits point P. There are few rays of light that reflect at such an angle that it enters the eye. But these rays are not bouncing off point P. Note that the surface normal is uniform throughout and all this is assuming angle of incidence = angle of reflection.

Again, can't it be possible to have a white surface that doesn't diffuse reflection? It would rather act like a mirror.
Exactly my thoughts. A smooth 'finish' to a glossy material can minimize diffuse reflection.


Anyway, the idea was not going into a debate of what material the object needs to be in order to be invisble. I just wanted to clarify my doubt of how we can see objects for which there may be no obvious ray trajectories using the law of reflection. I realise that the reason we still see these points is because of diffuse reflection from the surface, successive reflections from surrounding objects and perhaps scaterring of light by dust particles in the air.

Thanks a lot everybody :smile:
 
  • #10
russ_watters
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Again, can't it be possible to have a white surface that doesn't diffuse reflection? It would rather act like a mirror.
I have never heard of a color being associated with a mirror. It sounds like arguing against a definition to me.
Verminmox said:
Anyway, the idea was not going into a debate of what material the object needs to be in order to be invisble. I just wanted to clarify my doubt of how we can see objects for which there may be no obvious ray trajectories using the law of reflection.
If we change that one little phrase "white object" to "perfect mirror" in your first post, then the answer is no, we can't see the light.
 
  • #11
DaveC426913
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The only ray of light that I have shown in the diagram is the one which hits point P. There are few rays of light that reflect at such an angle that it enters the eye. But these rays are not bouncing off point P. Note that the surface normal is uniform throughout and all this is assuming angle of incidence = angle of reflection.
What is the significance of point P though? It's not where you will (or should) see the light. (This should be obvious during the day. Your reflective surface will reflect the distant horizon, and it that reflection, you will (and should) see the source of light slightly off to the side).

attachment.php?attachmentid=19028&stc=1&d=1242947010.gif
 

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  • #12
Mentallic
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If we assume perfect situations such that the same diagram the OP posted is in deep dark space, and it is a perfect mirror reflecting the light rays. However, there is a barrier between the observer and light source so that the light cannot travel directly to the observers eye. The reflective surface is also in such a position that it cannot be possible to reach the observer's eye through reflective positions.

Would the observer see nothing at all? Complete darkness?

I'm not sure if this would apply, but just putting it out there - as gravity can bend light, is it possible to bend the light enough so as to bend around the barrier or reflect and bend to reach the observers eye?
 
  • #13
diazona
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If we assume perfect situations such that the same diagram the OP posted is in deep dark space, and it is a perfect mirror reflecting the light rays. However, there is a barrier between the observer and light source so that the light cannot travel directly to the observers eye. The reflective surface is also in such a position that it cannot be possible to reach the observer's eye through reflective positions.

Would the observer see nothing at all? Complete darkness?
Yep, complete darkness. If no light rays can reach the observer's eye either directly or by reflection, the observer will not see any light.

I'm not sure if this would apply, but just putting it out there - as gravity can bend light, is it possible to bend the light enough so as to bend around the barrier or reflect and bend to reach the observers eye?
Sure, but depending on the distances involved you might need a black hole to do it. There's no object on Earth, or even in the solar system, that can bend light enough to detect without very sensitive measuring instruments.
 
  • #14
Mentallic
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Thanks for clearing that up for me diazona :smile:
 
  • #15
DaveC426913
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I have corrected the OP's original diagram.

attachment.php?attachmentid=19132&stc=1&d=1243523126.jpg
 

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